一类非自治微分积分方程的全局指数稳定性

马 超, 黎定仕

(西南交通大学数学学院,四川成都610031)

1 预备知识

微分积分方程稳定性的问题具有其特定的物理意义,许多学者对其进行了深入的探究[1-6].微分积分方程在多个科学领域中,如控制理论、生物、经济、医学等都会遇见,考虑其后效反应或者时滞状态[7-8]已经成为了必要.特别地,人们常常用微分积分方程来描述具有遗传性质的模型.而在这些领域中常见的时滞现象包括常数时滞和变量时滞[9-14],但是由于存在大量轴突大小和长度类似的路径,微分积分方程常常会有空间上的外延性.于是,会有沿着这些路径的传导速度和传播时滞的不同的现象产生.在这种情况下,信号的传播不再是瞬间的,也不能用离散时滞来模拟,从而就出现了一种更为合适的描述,即连续的分布式时滞.

本文研究如下非自治微分积分方程

2 主要结果

3 例子

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